Boundary Value Problems For Partial Differential Equations And Applications
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Partial Differential Equations And Boundary Value Problems With Applications
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Author : Mark A. Pinsky
language : en
Publisher:
Release Date : 2003
Partial Differential Equations And Boundary Value Problems With Applications written by Mark A. Pinsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Boundary value problems categories.
Boundary Value Problems For Partial Differential Equations And Applications
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Author : Jacques-Louis Lions
language : en
Publisher: Elsevier Masson
Release Date : 1993
Boundary Value Problems For Partial Differential Equations And Applications written by Jacques-Louis Lions and has been published by Elsevier Masson this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Boundary value problems categories.
Ordinary And Partial Differential Equations
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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-13
Ordinary And Partial Differential Equations written by Ravi P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-13 with Mathematics categories.
In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.
Partial Differential Equations And Boundary Value Problems With Applications
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Author : Mark A. Pinsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Partial Differential Equations And Boundary Value Problems With Applications written by Mark A. Pinsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Perturbation Of The Boundary In Boundary Value Problems Of Partial Differential Equations
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Author : Dan Henry
language : en
Publisher: Cambridge University Press
Release Date : 2005-05-26
Perturbation Of The Boundary In Boundary Value Problems Of Partial Differential Equations written by Dan Henry and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-26 with Mathematics categories.
This book, first published in 2005, works to answer a wide range of problems involving boundary perturbations in the study of partial differential equations.
Boundary Value Problems
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Author : David L. Powers
language : en
Publisher: Elsevier
Release Date : 2005-10-19
Boundary Value Problems written by David L. Powers and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-19 with Mathematics categories.
Boundary Value Problems, Fifth Edition, is the leading text on boundary value problems and Fourier series. The author, David Powers, has written a thorough theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that Powers is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering. His expertise is fully apparent in this updated text. The text progresses at a comfortable pace for undergraduates in engineering and mathematics, illustrating the classical methods with clear explanations and hundreds of exercises. This updated edition contains many new features, including nearly 900 exercises ranging in difficulty, chapter review questions, and many fully worked examples. This text is ideal for professionals and students in mathematics and engineering, especially those working with partial differential equations. - Nearly 900 exercises ranging in difficulty - Many fully worked examples
Initial Boundary Value Problems And The Navier Stokes Equation
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Author : Heinz-Otto Kreiss
language : en
Publisher: SIAM
Release Date : 2004-01-01
Initial Boundary Value Problems And The Navier Stokes Equation written by Heinz-Otto Kreiss and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Science categories.
Initial-Boundary Value Problems and the Navier-Stokes Equations gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs. Applications to parabolic and hyperbolic systems are emphasized in this text. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The book explains the principles of these subjects. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. Audience: when the book was written, the main intent was to write a text on initial-boundary value problems that was accessible to a rather wide audience. Functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplifications have been used throughout. This book continues to be useful to researchers and graduate students in applied mathematics and engineering.
Partial Differential Equations
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Author : Deborah E. Richards
language : en
Publisher: Nova Science Publishers
Release Date : 2015
Partial Differential Equations written by Deborah E. Richards and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
This book includes research on the Lax-Milgram theorem, which can be used to prove existence and uniqueness of weak solutions to partial differential equations and several examples of its application to relevant boundary value problems are presented. The authors also investigate nonlinear control problems for couple partial differential equations arising from climate and circulation dynamics in the equatorial zone; the integration of partial differential equations (PDE) with the help of non-commutative analysis over octonions and Cayley-Dickson algebras; and the existence and properties of solutions, applications in sequential optimal control with pointwise in time state constraints.
Non Homogeneous Boundary Value Problems And Applications
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Author : Jacques Louis Lions
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Homogeneous Boundary Value Problems And Applications written by Jacques Louis Lions and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
1. We describe, at first in a very formaI manner, our essential aim. n Let m be an op en subset of R , with boundary am. In m and on am we introduce, respectively, linear differential operators P and Qj' 0 ~ i ~ 'V. By "non-homogeneous boundary value problem" we mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be given in function space s F and G , F being a space" on m" and the G/ s spaces" on am" ; j we seek u in a function space u/t "on m" satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v«])). Qj may be identically zero on part of am, so that the number of boundary conditions may depend on the part of am considered 2. We take as "working hypothesis" that, for fEF and gjEG , j the problem (1), (2) admits a unique solution u E U/t, which depends 3 continuously on the data . But for alllinear probIems, there is a large number of choiees for the space s u/t and {F; G} (naturally linke d together). j Generally speaking, our aim is to determine families of spaces 'ft and {F; G}, associated in a "natural" way with problem (1), (2) and con j venient for applications, and also all possible choiees for u/t and {F; G} j in these families.
Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations
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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 1988-01-01
Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.